What drone note? The low E, or the high E harmonic? Low E, just leave it open. High E, play the E, and tap the 12th fret for the harmonic. You can also pluck the note with another finger behind the harmonic to form the harmonic.
His pinkie seems to be floating over a harmonic spot on the upper neck, and he flicks the lower strings (GBe?) with his fingers near the 12th fret. Maybe 5th fret harmonics combining with some funky 12th fret harmonics ringing out because of where he played and how hard he flicked the super-thin strings he uses?
Sounded frickin' cool, no matter what it was.